Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo

Dootika Vats; James M. Flegal; Galin L. Jones

doi:10.3150/16-BEJ914

Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo

Dootika Vats, James M. Flegal, Galin L. Jones

Statistics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and provide conditions for strong consistency. We examine the finite sample properties of the multivariate spectral variance estimators and its eigenvalues in the context of a vector autoregressive process of order 1.

Original language	English (US)
Pages (from-to)	1860-1909
Number of pages	50
Journal	Bernoulli
Volume	24
Issue number	3
DOIs	https://doi.org/10.3150/16-BEJ914
State	Published - Aug 2018

Bibliographical note

Funding Information:
The authors thank Tiefeng Jiang and Gongjun Xu for helpful discussions. The second author’s work is partially supported by NSF DMS-13-08270. The third author’s work is partially supported by NSF DMS-13-10096 and NIH NIBIB R01 EB012547.

Funding Information:
The authors thank Tiefeng Jiang and Gongjun Xu for helpful discussions. The second author?s work is partially supported by NSF DMS-13-08270. The third author?s work is partially supported by NSF DMS-13-10096 and NIH NIBIB R01 EB012547.

Publisher Copyright:
© 2018 ISI/BS.

Keywords

Markov chain
Monte Carlo
Spectral methods
Standard errors

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10.3150/16-BEJ914

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abstract = "Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and provide conditions for strong consistency. We examine the finite sample properties of the multivariate spectral variance estimators and its eigenvalues in the context of a vector autoregressive process of order 1.",

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doi = "10.3150/16-BEJ914",

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AU - Flegal, James M.

AU - Jones, Galin L.

N1 - Funding Information: The authors thank Tiefeng Jiang and Gongjun Xu for helpful discussions. The second author’s work is partially supported by NSF DMS-13-08270. The third author’s work is partially supported by NSF DMS-13-10096 and NIH NIBIB R01 EB012547. Funding Information: The authors thank Tiefeng Jiang and Gongjun Xu for helpful discussions. The second author?s work is partially supported by NSF DMS-13-08270. The third author?s work is partially supported by NSF DMS-13-10096 and NIH NIBIB R01 EB012547. Publisher Copyright: © 2018 ISI/BS.

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AB - Markov chain Monte Carlo (MCMC) algorithms are used to estimate features of interest of a distribution. The Monte Carlo error in estimation has an asymptotic normal distribution whose multivariate nature has so far been ignored in the MCMC community. We present a class of multivariate spectral variance estimators for the asymptotic covariance matrix in the Markov chain central limit theorem and provide conditions for strong consistency. We examine the finite sample properties of the multivariate spectral variance estimators and its eigenvalues in the context of a vector autoregressive process of order 1.

KW - Markov chain

KW - Monte Carlo

KW - Spectral methods

KW - Standard errors

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Strong consistency of multivariate spectral variance estimators in Markov chain Monte Carlo

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